[GAP Forum] Diagonalize of symmetric matrix 248x248

[Mathieu Dutour]

Maybe you can try to use real arithmetic for diagonalization using a
Fortran code that implement Jacobi method.

Otherwise, I am not sure if such a diagonalization makes sense.
Such gram matrix are defined up to arithmetic equivalence
A ---> PAP^T   with P an integral matrix of determinant +-1.
The matrix on Nebe's website is just one matrix in the whole equivalence
class and the eigenvalues will be different if you choose another matrix in
the equivalence class.

  Mathieu



On Sat, Jan 12, 2013 at 9:23 PM, Marek Mitros <marek at mitros.org> wrote:

> Hi,
>
> What is the quickest way to diagonalize symmetric matrix 248x248 with
> integral entries. I run Eigenvectors(Rationals, m) but it run long
> time on my PC. The matrix is the Gram matrix of Thompson Smith lattice
> in dimension 248. See page:
> http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/TH.html
>
> I would like to obtain the lattice generators or alternatively
> orthogonal representation of Thompson sporadic group.
>
> Regards,
> Marek
>
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